citation needed for your first point: "Companies extract money from the stock market by issuing IPOs, after that happens, it doesn't matter to them very much at what price their shares are traded"
It matters to the people running those companies (Because they own a lot of stock, or work for people who own a lot of stock). It matters less for the firms, themselves.
A high stock price prevents a corporate takeover (which is not a real-world-value-destroying activity - factories operated by a company don't burn up when it happens), and it makes it possible for the firm to raise money by selling stock. In a world of low interest rates, and easy credit, this is not very important.
A high stock price prevents a corporate takeover (which is not a real-world-value-destroying activity - factories operated by a company don't burn up when it happens), and it makes it possible for the firm to raise money by selling stock. In a world of low interest rates, and easy credit, this is not very important.